Question

The value of $\log 2+2\left(\frac{1}{5}+\frac{1}{3}\cdot \frac{1}{5^3}+\frac{1}{5}\cdot \frac{1}{5^5}+\dots \right)$ is

• A. $\log 2+\log 3$
• B. $\log 2+2$
• C. $\frac{1}{2}\log 2$
• D. $\log 3$

Answer 1

Answer: (D)

$\log 2+2\left(\frac{1}{5}+\frac{1}{3}\cdot \frac{1}{5^3}+\frac{1}{5}\cdot \frac{1}{5^5}+\dots \infty \right)$
$=\log 2+\log \left(\frac{1+\frac{1}{5}}{1-\frac{1}{5}}\right)$
$=\log 2+\log \left(\frac{3}{2}\right)=\log 3$